Analysis of a model of phosphorus uptake by plant roots

Myriam Comte (1) , Jean-Michel Coron (1) , Sergio Guerrero (1) , Pierre-Henri Tournier (1)

1 LJLL - Laboratoire Jacques-Louis Lions

In this paper, we consider a model of phosphorus uptake by plant roots, governed by a quasilinear parabolic equation. We first study the well-posedness of the associated Cauchy problem. Then, we consider a shape optimization problem: how to deform the shape of the root in order to increase phosphorus uptake. Finally, we give some numerical results of the shape optimization process.

Mots clés: Quasilinear parabolic equations; Regularity estimates; Phosphorus uptake; Plant roots; Shape optimization

Domaines: Analyse numérique [cs.NA]

Myriam Comte, Jean-Michel Coron, Sergio Guerrero, Pierre-Henri Tournier. Analysis of a model of phosphorus uptake by plant roots. Journal of Evolution Equations, 2013, 13, pp.595-615. ⟨hal-00739873⟩